Motion of Inextensible Quaternionic Curves and Modified Korteweg-de Vries Equation

[1] D. J. Korteweg, G. De Vries, On the Change of Form of Long Waves Advancing in a Rectangular Canal, and on a New Type of Long Stationary Waves. Philos. Magazine 39 (1895), 422–443. Search in Google Scholar

[2] T. Geyikli, Finite Element Studies of the mKdV Equation[Dissertation]. UK, Bangor, University College of North Wales, 1994. Search in Google Scholar

[3] M. Dehghan, A. Shokri, A Numerical Method for KdV Equation Using Collocation. Nonlinear Dynamics 50 (2007), 111–120. Search in Google Scholar

[4] A. M. Wazwaz, Partial Differential Equations and Solitary Waves Theory. Higher Education Press, Beijing and Springer-Verlag, Berlin Heidelberg, 2009.10.1007/978-3-642-00251-9 Search in Google Scholar

[5] S. Islam, K. Khan, M. A. Akbar, An Analytical Method for Finding Exact Solutions of Modified Kortewegde Vries Equation. Results in Physics 5 (2015), 131–135. Search in Google Scholar

[6] E. Previato, Geometry of the Modified KdV Equation. Lecture Notes in Physics 424 (1993), 43–65.10.1007/BFb0021441 Search in Google Scholar

[7] M. Wadati, The Modified Korteweg-de Vries Equation. J. Phys. Soc. Japan 34(5) (1973), 1289–1296.10.1143/JPSJ.34.1289 Search in Google Scholar

[8] S. Tek, Modified Korteweg-de Vries Surfaces. J. Math. Physics 48 (2007), 013505.10.1063/1.2409523 Search in Google Scholar

[9] C. Rogers, W. K. Schief, Bäcklund and Darboux Transformations, Geometry and Modern Applications in Soliton Theory. Cambridge University Press, 2002.10.1017/CBO9780511606359 Search in Google Scholar

[10] N. Hayashi, P. Naumkin, On the Modified KortewegDe Vries Equation. Math. Phys. Anal. Geom. 4(3) (2001), 197–227.10.1023/A:1012953917956 Search in Google Scholar

[11] W. R. Hamilton, Elements of Quaternions. Chelsea, New York, 1899. Search in Google Scholar

[12] M. Akyiğit, H. H. Kösal, M. Tosun, Split Fibonacci Quaternions. Adv. Appl. Clifford Algebras 23 (2013), 535545.10.1007/s00006-013-0401-9 Search in Google Scholar

[13] K. E. Özen, M. Tosun, Fibonacci Elliptic Biquaternions. Fundam. J. Math. Applications 4(1) (2021), 1016.10.33401/fujma.811058 Search in Google Scholar

[14] K. Bharathi, M. Nagaraj, Quaternion Valued Function of a Real Serret-Frenet Formulae. Indian J. Pure Appl. Mathematics 16 (1985), 741756. Search in Google Scholar

[15] S. Demir, Physical Applications of Complex and Dual Quaternions [Dissertation]. Turkey: Anadolu University, 2003. Search in Google Scholar

[16] Ö. G. Yıldız, Ö. Içer, A Note on Evolution of Quaternionic Curves in the Euclidean Space. Konuralp J. Mathematics 7(2) (2019), 462469. Search in Google Scholar

[17] T. Soyfidan, H. Parlatici, M. A. Güngör, On the Quaternionic Curves According to Parallel Transport Frame. TWMS J. Pure Appl. Mathematics 4(2) (2013), 194203. Search in Google Scholar

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